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Hyperintensional logics for everyone

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Igor Sedlár at The Czech Academy of Sciences
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We introduce a general representation of unary hyperintensional modalities and study various hyperintensional modal logics based on the representation. It is shown that the major approaches to hyperintensionality known from the literature, that is state-based, syntactic and structuralist approaches, all correspond to special cases of the general framework. Completeness results pertaining to our hyperintensional modal logics are established.
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Synthese (2021) 198:933–956
https://doi.org/10.1007/s11229-018-02076-7
Hyperintensional logics for everyone
Igor Sedlár1
Received: 1 March 2017 / Accepted: 26 December 2018 / Published online: 12 January 2019
© Springer Nature B.V. 2019
Abstract
We introduce a general representation of unary hyperintensional modalities and study
various hyperintensional modal logics based on the representation. It is shown that the
major approaches to hyperintensionality known from the literature, that is state-based,
syntactic and structuralist approaches, all correspond to special cases of the general
framework. Completeness results pertaining to our hyperintensional modal logics are
established.
Keywords Awareness logic ·Hyperintensionality ·Hyperintensional logic ·
Hyperintensional modalities ·Impossible worlds ·Modal logic ·Non-Fregean logic ·
Structured propositions
1 Introduction
The possible-worlds framework has provided semantics for various formal languages
as well as large portions of natural language. The general strategy is to represent
semantic contents of expressions by intensions, i.e. functions from possible worlds
(usually taken as unanalysed indices) to extensions. The specific kind of extension
depends on the kind of expression at hand. For instance, extensions are truth-values
0,1 in the case of sentences, individuals (from some fixed domain) in the case of names
and n-ary relations in the case of n-ary predicates. Modalities are seen as expressing
properties of (or relations between) intensions; the corresponding intensions are func-
tions from possible worlds to relations on intensions. In the case of unary sentential
modalities, an equivalent approach is to take functions from possible worlds to sets of
propositions (i.e. to sets of sets of possible worlds).
A prominent example of this approach is the Montague–Scott semantics for modal
logic (Montague 1968; Scott 1970; Segerberg 1971; Chellas 1980; Pacuit 2017). In
BIgor Sedlár
sedlar@cs.cas.cz
1Institute of Computer Science, The Czech Academy of Sciences, Pod Vodárenskou vˇeží 2,
182 07 Prague 8, Czech Republic
123
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